The overall goals of the Center and the individual specific aims of essentially all projects and cores requires quantitative tools, such as statistical aspects of experimental design and analysis, the development of optimal experimental methods, and deterministic and stochastic modeling of exposure and health. The purpose of the Mathematical and Statistical Analysis and Modeling (MSAM) Core is efficiently provide these services, which will improve the overall quality of the work being performed and build strong relationships among Center projects. An interdisciplinary group of environmental modelers, biostatisticians, and mathematicians, who together have the requisite experience and training to accomplish the goals of the MSAM Core, will join together in a collaborative team to provide a broad range of services to the Center. The overall goal of this project can be divided into the following specific aims: (1) to assist Center researchers with experimental design; (2) to aid Center researchers with the analysis of experimental data and the formation of statistical inferences; (3) to assist with the development of methods for optimal use of complex measurement devices (e.g, X-ray attenuation); (4) to develop methods for biological transformations and mass transfer phenomena; (5) to collaborate with Center researchers on the development of sophisticated models of exposure; (6) to provide numerical methods support for stochastic exposure and health modeling; and (7) to obtain specialized mathematical and statistical software and models (e.g., pharmacokinetic models) and work with Center researchers on the use of such tools. The specific aims of this project will be met through assembling a team that has broad expertise in all aspects of environmental modeling, including: statistical analysis of experimental design and analysis, deterministic and stochastic environmental modeling, including: statistical analysis of experimental design, and deterministic and stochastic model formulation, numerical solution approaches, error estimation, adaptive grid refinement, homogenization method, spatial/temporal estimation methods, and composition exposure modeling. The expertise offered by the collection of personnel on this Core is both broad and deep, which will add significant strength to the Center.